Decorrelation-Based Feature Discovery: Saliva-Whole

1 Effect of UPSTM-Based Decorrelation on Feature Discovery

1.0.1 Loading the libraries

library("FRESA.CAD")
library(readxl)
library(igraph)
library(umap)
library(tsne)
library(entropy)

op <- par(no.readonly = TRUE)
pander::panderOptions('digits', 3)
pander::panderOptions('table.split.table', 400)
pander::panderOptions('keep.trailing.zeros',TRUE)

1.1 Material and Methods

1.2 Data: The COVID_19 Data-Set

The data to process is described in:

https://zenodo.org/record/4156647#.Y1bSF3bMKUk

IR Saliva Testing Dataset

10.5281/zenodo.4156647 https://doi.org/10.5281/zenodo.4156647

I added a column to the data identifying the repeated experiments.

SalivaIR <- as.data.frame(read_excel("~/GitHub/FCA/Data/SalivaThermal_Source_Data_2.xlsx"))


SalivaIR_set1 <- subset(SalivaIR,RepID==1)
rownames(SalivaIR_set1) <- SalivaIR_set1$ID
SalivaIR_set1$RepID <- NULL
SalivaIR_set1$ID <- NULL
SalivaIR_set1$Ct <- NULL

SalivaIR_set2 <- subset(SalivaIR,RepID==2)
rownames(SalivaIR_set2) <- SalivaIR_set2$ID
SalivaIR_set2$RepID <- NULL
SalivaIR_set2$ID <- NULL
SalivaIR_set2$Ct <- NULL

SalivaIR_set3 <- subset(SalivaIR,RepID==3)
rownames(SalivaIR_set3) <- SalivaIR_set3$ID
SalivaIR_set3$RepID <- NULL
SalivaIR_set3$ID <- NULL
SalivaIR_set3$Ct <- NULL

SalivaIR_Avg <- (SalivaIR_set1 + SalivaIR_set2 + SalivaIR_set3)/3


colnames(SalivaIR_Avg) <- paste("V",colnames(SalivaIR_Avg),sep="_")

SalivaIR_Avg$class <- 1*(str_detect(rownames(SalivaIR_Avg),"P"))

pander::pander(table(SalivaIR_Avg$class))

0	1
30	31

1.2.0.1 Standarize the names for the reporting

studyName <- "IRSaliva"
dataframe <- SalivaIR_Avg
outcome <- "class"

TopVariables <- 10

thro <- 0.80
cexheat = 0.15

1.3 Generaring the report

1.3.1 Libraries

Some libraries

library(psych)
library(whitening)
library("vioplot")
library("rpart")

1.3.2 Data specs

pander::pander(c(rows=nrow(dataframe),col=ncol(dataframe)-1))

rows	col
61	251

pander::pander(table(dataframe[,outcome]))

0	1
30	31

varlist <- colnames(dataframe)
varlist <- varlist[varlist != outcome]

largeSet <- length(varlist) > 1500 

1.3.3 Scaling the data

Scaling and removing near zero variance columns and highly co-linear(r>0.99999) columns

  ### Some global cleaning
  sdiszero <- apply(dataframe,2,sd) > 1.0e-16
  dataframe <- dataframe[,sdiszero]

  varlist <- colnames(dataframe)[colnames(dataframe) != outcome]
  tokeep <- c(as.character(correlated_Remove(dataframe,varlist,thr=0.99999)),outcome)
  dataframe <- dataframe[,tokeep]

  varlist <- colnames(dataframe)
  varlist <- varlist[varlist != outcome]
  
  iscontinous <- sapply(apply(dataframe,2,unique),length) >= 5 ## Only variables with enough samples



dataframeScaled <- FRESAScale(dataframe,method="OrderLogit")$scaledData

1.4 The heatmap of the data

numsub <- nrow(dataframe)
if (numsub > 1000) numsub <- 1000


if (!largeSet)
{

  hm <- heatMaps(data=dataframeScaled[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 xlab="Feature",
                 ylab="Sample",
                 srtCol=45,
                 srtRow=45,
                 cexCol=cexheat,
                 cexRow=cexheat
                 )
  par(op)
}

1.4.0.1 Correlation Matrix of the Data

The heat map of the data

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  #cormat <- Rfast::cora(as.matrix(dataframe[,varlist]),large=TRUE)
  cormat <- cor(dataframe[,varlist],method="pearson")
  cormat[is.na(cormat)] <- 0
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Original Correlation",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.999994

1.5 The decorrelation

DEdataframe <- IDeA(dataframe,verbose=TRUE,thr=thro)
#> 
#>  Included: 224 , Uni p: 0.04988877 , Uncorrelated Base: 1 , Outcome-Driven Size: 0 , Base Size: 1 
#> 
#> 
 1 <R=1.000,r=0.975,N=  224>, Top: 2( 53 )[ 1 : 2 Fa= 2 : 0.975 ]( 2 , 147 , 0 ),<|>Tot Used: 149 , Added: 147 , Zero Std: 0 , Max Cor: 1.000
#> 
 2 <R=1.000,r=0.975,N=  224>, Top: 9( 74 )[ 1 : 9 Fa= 11 : 0.975 ]( 9 , 121 , 2 ),<|>Tot Used: 224 , Added: 121 , Zero Std: 0 , Max Cor: 1.000
#> 
 3 <R=1.000,r=0.975,N=  224>, Top: 27( 9 )[ 1 : 27 Fa= 38 : 0.975 ]( 27 , 100 , 11 ),<|>Tot Used: 224 , Added: 100 , Zero Std: 0 , Max Cor: 1.000
#> 
 4 <R=1.000,r=0.975,N=  224>, Top: 46( 5 )=[ 2 : 46 Fa= 83 : 0.989 ]( 45 , 90 , 38 ),<|>Tot Used: 224 , Added: 90 , Zero Std: 0 , Max Cor: 1.000
#> 
 5 <R=1.000,r=0.975,N=  224>, Top: 23( 2 )[ 1 : 23 Fa= 106 : 0.975 ]( 23 , 36 , 83 ),<|>Tot Used: 224 , Added: 36 , Zero Std: 0 , Max Cor: 0.999
#> 
 6 <R=0.999,r=0.974,N=  224>, Top: 11( 1 )[ 1 : 11 Fa= 116 : 0.974 ]( 11 , 12 , 106 ),<|>Tot Used: 224 , Added: 12 , Zero Std: 0 , Max Cor: 0.996
#> 
 7 <R=0.996,r=0.948,N=  118>, Top: 51( 1 )[ 1 : 51 Fa= 125 : 0.948 ]( 50 , 57 , 116 ),<|>Tot Used: 224 , Added: 57 , Zero Std: 0 , Max Cor: 0.998
#> 
 8 <R=0.998,r=0.949,N=  118>, Top: 30( 1 )[ 1 : 30 Fa= 132 : 0.949 ]( 30 , 33 , 125 ),<|>Tot Used: 224 , Added: 33 , Zero Std: 0 , Max Cor: 0.992
#> 
 9 <R=0.992,r=0.946,N=  118>, Top: 19( 1 )[ 1 : 19 Fa= 134 : 0.946 ]( 18 , 21 , 132 ),<|>Tot Used: 224 , Added: 21 , Zero Std: 0 , Max Cor: 0.991
#> 
 10 <R=0.991,r=0.945,N=  118>, Top: 3( 1 )[ 1 : 3 Fa= 134 : 0.945 ]( 3 , 3 , 134 ),<|>Tot Used: 224 , Added: 3 , Zero Std: 0 , Max Cor: 0.966
#> 
 11 <R=0.966,r=0.883,N=  106>, Top: 42( 1 )[ 1 : 42 Fa= 141 : 0.883 ]( 41 , 56 , 134 ),<|>Tot Used: 224 , Added: 56 , Zero Std: 0 , Max Cor: 0.972
#> 
 12 <R=0.972,r=0.886,N=  106>, Top: 13( 1 )[ 1 : 13 Fa= 143 : 0.886 ]( 12 , 13 , 141 ),<|>Tot Used: 224 , Added: 13 , Zero Std: 0 , Max Cor: 0.925
#> 
 13 <R=0.925,r=0.863,N=  106>, Top: 24( 1 )[ 1 : 24 Fa= 145 : 0.863 ]( 23 , 26 , 143 ),<|>Tot Used: 224 , Added: 26 , Zero Std: 0 , Max Cor: 0.992
#> 
 14 <R=0.992,r=0.896,N=  106>, Top: 4( 1 )[ 1 : 4 Fa= 145 : 0.896 ]( 4 , 4 , 145 ),<|>Tot Used: 224 , Added: 4 , Zero Std: 0 , Max Cor: 0.976
#> 
 15 <R=0.976,r=0.838,N=   44>, Top: 21( 1 )[ 1 : 21 Fa= 145 : 0.838 ]( 21 , 23 , 145 ),<|>Tot Used: 224 , Added: 23 , Zero Std: 0 , Max Cor: 0.974
#> 
 16 <R=0.974,r=0.837,N=   44>, Top: 7( 1 )[ 1 : 7 Fa= 146 : 0.837 ]( 7 , 7 , 145 ),<|>Tot Used: 224 , Added: 7 , Zero Std: 0 , Max Cor: 0.894
#> 
 17 <R=0.894,r=0.800,N=   44>, Top: 29( 2 )[ 1 : 29 Fa= 147 : 0.800 ]( 26 , 32 , 146 ),<|>Tot Used: 224 , Added: 32 , Zero Std: 0 , Max Cor: 0.973
#> 
 18 <R=0.973,r=0.837,N=   44>, Top: 5( 1 )[ 1 : 5 Fa= 149 : 0.837 ]( 5 , 6 , 147 ),<|>Tot Used: 224 , Added: 6 , Zero Std: 0 , Max Cor: 0.955
#> 
 19 <R=0.955,r=0.827,N=   44>, Top: 1( 1 )[ 1 : 1 Fa= 149 : 0.827 ]( 1 , 1 , 149 ),<|>Tot Used: 224 , Added: 1 , Zero Std: 0 , Max Cor: 0.825
#> 
 20 <R=0.825,r=0.800,N=    7>, Top: 3( 1 )[ 1 : 3 Fa= 150 : 0.800 ]( 3 , 4 , 149 ),<|>Tot Used: 224 , Added: 4 , Zero Std: 0 , Max Cor: 0.881
#> 
 21 <R=0.881,r=0.800,N=    7>, Top: 2( 1 )[ 1 : 2 Fa= 150 : 0.800 ]( 2 , 2 , 150 ),<|>Tot Used: 224 , Added: 2 , Zero Std: 0 , Max Cor: 0.795
#> 
 22 <R=0.795,r=0.800,N=    0>
#> 
 [ 22 ], 0.7947222 Decor Dimension: 224 Nused: 224 . Cor to Base: 56 , ABase: 1 , Outcome Base: 0 
#> 
varlistc <- colnames(DEdataframe)[colnames(DEdataframe) != outcome]

pander::pander(sum(apply(dataframe[,varlist],2,var)))

5.5

pander::pander(sum(apply(DEdataframe[,varlistc],2,var)))

0.0295

pander::pander(entropy(discretize(unlist(dataframe[,varlist]), 256)))

5.08

pander::pander(entropy(discretize(unlist(DEdataframe[,varlistc]), 256)))

0.643

1.5.1 The decorrelation matrix

if (!largeSet)
{

  par(cex=0.6,cex.main=0.85,cex.axis=0.7)
  
  UPSTM <- attr(DEdataframe,"UPSTM")
  
  gplots::heatmap.2(1.0*(abs(UPSTM)>0),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Decorrelation matrix",
                    cexRow = cexheat,
                    cexCol = cexheat,
                   srtCol=45,
                   srtRow=45,
                    key.title=NA,
                    key.xlab="|Beta|>0",
                    xlab="Output Feature", ylab="Input Feature")
  
  par(op)
}

1.6 The heatmap of the decorrelated data

if (!largeSet)
{

  hm <- heatMaps(data=DEdataframe[1:numsub,],
                 Outcome=outcome,
                 Scale=TRUE,
                 hCluster = "row",
                 cexRow = cexheat,
                 cexCol = cexheat,
                 srtCol=45,
                 srtRow=45,
                 xlab="Feature",
                 ylab="Sample")
  par(op)
}

1.7 The correlation matrix after decorrelation

if (!largeSet)
{

  cormat <- cor(DEdataframe[,varlistc],method="pearson")
  cormat[is.na(cormat)] <- 0
  
  gplots::heatmap.2(abs(cormat),
                    trace = "none",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "Correlation after IDeA",
                    cexRow = cexheat,
                    cexCol = cexheat,
                     srtCol=45,
                     srtRow=45,
                    key.title=NA,
                    key.xlab="|Pearson Correlation|",
                    xlab="Feature", ylab="Feature")
  
  par(op)
  diag(cormat) <- 0
  print(max(abs(cormat)))
}

[1] 0.7947222

1.8 U-MAP Visualization of features

1.8.1 The UMAP based on LASSO on Raw Data

if (nrow(dataframe) < 1000)
{
  classes <- unique(dataframe[1:numsub,outcome])
  raincolors <- rainbow(length(classes))
  names(raincolors) <- classes
  datasetframe.umap = umap(scale(dataframe[1:numsub,varlist]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: Original",t='n')
  text(datasetframe.umap$layout,labels=dataframe[1:numsub,outcome],col=raincolors[dataframe[1:numsub,outcome]+1])
}

1.8.2 The decorralted UMAP

if (nrow(dataframe) < 1000)
{

  datasetframe.umap = umap(scale(DEdataframe[1:numsub,varlistc]),n_components=2)
  plot(datasetframe.umap$layout,xlab="U1",ylab="U2",main="UMAP: After IDeA",t='n')
  text(datasetframe.umap$layout,labels=DEdataframe[1:numsub,outcome],col=raincolors[DEdataframe[1:numsub,outcome]+1])
}

1.9 Univariate Analysis

1.9.1 Univariate

univarRAW <- uniRankVar(varlist,
               paste(outcome,"~1"),
               outcome,
               dataframe,
               rankingTest="AUC")

100 : V_1064 200 : V_854

univarDe <- uniRankVar(varlistc,
               paste(outcome,"~1"),
               outcome,
               DEdataframe,
               rankingTest="AUC",
               )

100 : La_V_1064 200 : La_V_854

1.9.2 Final Table

univariate_columns <- c("caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC")

##top variables
topvar <- c(1:length(varlist)) <= TopVariables
tableRaw <- univarRAW$orderframe[topvar,univariate_columns]
pander::pander(tableRaw)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
V_908	0.221	0.128	0.261	0.117	0.579	0.596
V_906	0.220	0.127	0.261	0.117	0.585	0.596
V_904	0.220	0.127	0.261	0.117	0.592	0.596
V_892	0.219	0.127	0.261	0.121	0.626	0.596
V_890	0.219	0.127	0.261	0.121	0.616	0.596
V_888	0.219	0.127	0.261	0.122	0.603	0.596
V_912	0.223	0.129	0.263	0.117	0.604	0.595
V_910	0.222	0.128	0.262	0.117	0.587	0.595
V_896	0.220	0.127	0.261	0.120	0.620	0.595
V_894	0.219	0.127	0.261	0.121	0.625	0.595

topLAvar <- univarDe$orderframe$Name[str_detect(univarDe$orderframe$Name,"La_")]
topLAvar <- unique(c(univarDe$orderframe$Name[topvar],topLAvar[1:as.integer(TopVariables/2)]))
finalTable <- univarDe$orderframe[topLAvar,univariate_columns]


pander::pander(finalTable)

	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC
La_V_984	-1.77e-04	5.79e-04	5.00e-04	6.60e-04	0.0433	0.810
La_V_926	3.01e-06	1.00e-05	1.32e-05	1.06e-05	0.8339	0.791
La_V_1204	-1.17e-06	1.26e-05	-1.46e-05	1.21e-05	0.8554	0.789
La_V_888	-4.82e-05	4.51e-04	2.98e-04	2.26e-04	0.5083	0.782
La_V_1110	2.65e-05	8.94e-05	-5.42e-05	9.75e-05	0.0657	0.778
La_V_924	-1.77e-05	6.72e-04	-4.71e-04	6.34e-04	0.1659	0.778
La_V_1214	5.07e-04	1.13e-03	1.42e-03	8.02e-04	0.7269	0.762
La_V_964	1.27e-03	2.00e-03	-5.81e-04	2.04e-03	0.3591	0.759
La_V_1172	3.52e-06	3.58e-04	1.13e-04	1.78e-04	0.2284	0.742
La_V_1096	-2.02e-03	1.59e-02	-9.15e-03	1.07e-02	0.1704	0.733

dc <- getLatentCoefficients(DEdataframe)
fscores <- attr(DEdataframe,"fscore")


pander::pander(c(mean=mean(sapply(dc,length)),total=length(dc),fraction=length(dc)/(ncol(dataframe)-1)))

mean	total	fraction
4.83	223	0.996

theCharformulas <- attr(dc,"LatentCharFormulas")


finalTable <- rbind(finalTable,tableRaw[topvar[!(topvar %in% topLAvar)],univariate_columns])


orgnamez <- rownames(finalTable)
orgnamez <- str_remove_all(orgnamez,"La_")
finalTable$RAWAUC <- univarRAW$orderframe[orgnamez,"ROCAUC"]
finalTable$DecorFormula <- theCharformulas[rownames(finalTable)]
finalTable$fscores <- fscores[rownames(finalTable)]

Final_Columns <- c("DecorFormula","caseMean","caseStd","controlMean","controlStd","controlKSP","ROCAUC","RAWAUC","fscores")

finalTable <- finalTable[order(-finalTable$ROCAUC),]
pander::pander(finalTable[,Final_Columns])

	DecorFormula	caseMean	caseStd	controlMean	controlStd	controlKSP	ROCAUC	RAWAUC	fscores
La_V_984	+ (0.025)V_1138 - (0.040)V_1032 + V_984 - (0.987)V_982	-1.77e-04	5.79e-04	5.00e-04	6.60e-04	0.0433	0.810	0.582	-3
La_V_926	+ (0.138)V_930 - (0.604)V_928 + V_926 - (0.752)V_924 + (0.217)V_922 - (3.18e-05)V_878	3.01e-06	1.00e-05	1.32e-05	1.06e-05	0.8339	0.791	0.589	-5
La_V_1204	- (4.11e-04)V_1300 - (0.262)V_1206 + V_1204 - (1.415)V_1202 + (0.882)V_1200 - (0.205)V_1198	-1.17e-06	1.26e-05	-1.46e-05	1.21e-05	0.8554	0.789	0.560	-5
La_V_888	+ V_888 - (1.657)V_884 + (0.655)V_878	-4.82e-05	4.51e-04	2.98e-04	2.26e-04	0.5083	0.782	0.596	1
La_V_1110	- (5.55e-04)V_1138 + V_1110 - (1.754)V_1108 + (0.806)V_1104 + (1.084)V_1096 - (1.962)V_1094 + (0.826)V_1092	2.65e-05	8.94e-05	-5.42e-05	9.75e-05	0.0657	0.778	0.561	-5
La_V_924	+ V_924 - (0.999)V_922 - (4.98e-03)V_878	-1.77e-05	6.72e-04	-4.71e-04	6.34e-04	0.1659	0.778	0.588	1
La_V_1214	+ (0.040)V_1300 - (1.033)V_1216 + V_1214	5.07e-04	1.13e-03	1.42e-03	8.02e-04	0.7269	0.762	0.556	2
La_V_964	+ (0.069)V_1138 - (1.035)V_972 + V_964 - (6.837)V_878 + (6.813)V_876	1.27e-03	2.00e-03	-5.81e-04	2.04e-03	0.3591	0.759	0.585	0
La_V_1172	+ (3.03e-04)V_1300 + (0.970)V_1176 - (1.971)V_1174 + V_1172	3.52e-06	3.58e-04	1.13e-04	1.78e-04	0.2284	0.742	0.559	-1
La_V_1096	+ (11.525)V_1138 - (12.543)V_1136 + V_1096	-2.02e-03	1.59e-02	-9.15e-03	1.07e-02	0.1704	0.733	0.559	13
V_908	NA	2.21e-01	1.28e-01	2.61e-01	1.17e-01	0.5785	0.596	0.596	NA
V_906	NA	2.20e-01	1.27e-01	2.61e-01	1.17e-01	0.5848	0.596	0.596	NA
V_904	NA	2.20e-01	1.27e-01	2.61e-01	1.17e-01	0.5918	0.596	0.596	NA
V_892	NA	2.19e-01	1.27e-01	2.61e-01	1.21e-01	0.6256	0.596	0.596	NA
V_890	NA	2.19e-01	1.27e-01	2.61e-01	1.21e-01	0.6163	0.596	0.596	NA
V_888	NA	2.19e-01	1.27e-01	2.61e-01	1.22e-01	0.6032	0.596	0.596	NA
V_912	NA	2.23e-01	1.29e-01	2.63e-01	1.17e-01	0.6041	0.595	0.595	NA
V_910	NA	2.22e-01	1.28e-01	2.62e-01	1.17e-01	0.5866	0.595	0.595	NA
V_896	NA	2.20e-01	1.27e-01	2.61e-01	1.20e-01	0.6202	0.595	0.595	NA
V_894	NA	2.19e-01	1.27e-01	2.61e-01	1.21e-01	0.6248	0.595	0.595	NA

1.10 Comparing IDeA vs PCA vs EFA

1.10.1 PCA

featuresnames <- colnames(dataframe)[colnames(dataframe) != outcome]
pc <- prcomp(dataframe[,iscontinous],center = TRUE,scale. = TRUE)   #principal components
predPCA <- predict(pc,dataframe[,iscontinous])
PCAdataframe <- as.data.frame(cbind(predPCA,dataframe[,!iscontinous]))
colnames(PCAdataframe) <- c(colnames(predPCA),colnames(dataframe)[!iscontinous]) 
#plot(PCAdataframe[,colnames(PCAdataframe)!=outcome],col=dataframe[,outcome],cex=0.65,cex.lab=0.5,cex.axis=0.75,cex.sub=0.5,cex.main=0.75)

#pander::pander(pc$rotation)


PCACor <- cor(PCAdataframe[,colnames(PCAdataframe) != outcome])


  gplots::heatmap.2(abs(PCACor),
                    trace = "none",
  #                  scale = "row",
                    mar = c(5,5),
                    col=rev(heat.colors(5)),
                    main = "PCA Correlation",
                    cexRow = 0.5,
                    cexCol = 0.5,
                     srtCol=45,
                     srtRow= -45,
                    key.title=NA,
                    key.xlab="Pearson Correlation",
                    xlab="Feature", ylab="Feature")

1.10.2 EFA

EFAdataframe <- dataframeScaled

if (length(iscontinous) < 2000)
{
  topred <- min(length(iscontinous),nrow(dataframeScaled),ncol(predPCA)/2)
  if (topred < 2) topred <- 2
  
  uls <- fa(dataframeScaled[,iscontinous],nfactors=topred,rotate="varimax",warnings=FALSE)  # EFA analysis
  predEFA <- predict(uls,dataframeScaled[,iscontinous])
  EFAdataframe <- as.data.frame(cbind(predEFA,dataframeScaled[,!iscontinous]))
  colnames(EFAdataframe) <- c(colnames(predEFA),colnames(dataframeScaled)[!iscontinous]) 


  
  EFACor <- cor(EFAdataframe[,colnames(EFAdataframe) != outcome])
  
  
    gplots::heatmap.2(abs(EFACor),
                      trace = "none",
    #                  scale = "row",
                      mar = c(5,5),
                      col=rev(heat.colors(5)),
                      main = "EFA Correlation",
                      cexRow = 0.5,
                      cexCol = 0.5,
                       srtCol=45,
                       srtRow= -45,
                      key.title=NA,
                      key.xlab="Pearson Correlation",
                      xlab="Feature", ylab="Feature")
}

1.11 Effect on CAR modeling

par(op)
par(xpd = TRUE)
dataframe[,outcome] <- factor(dataframe[,outcome])
rawmodel <- rpart(paste(outcome,"~."),dataframe,control=rpart.control(maxdepth=3))
pr <- predict(rawmodel,dataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(rawmodel,main="Raw",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(rawmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,dataframe[,outcome]==0))
  }

pander::pander(table(dataframe[,outcome],pr))

	0	1
0	30	0
1	17	14

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.721	0.592	0.829
3	se	0.452	0.273	0.640
4	sp	1.000	0.884	1.000
6	diag.or	Inf	NA	Inf

par(op)
par(xpd = TRUE)
DEdataframe[,outcome] <- factor(DEdataframe[,outcome])
IDeAmodel <- rpart(paste(outcome,"~."),DEdataframe,control=rpart.control(maxdepth=3))
pr <- predict(IDeAmodel,DEdataframe,type = "class")

  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(IDeAmodel,main="IDeA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(IDeAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,DEdataframe[,outcome]==0))
  }

pander::pander(table(DEdataframe[,outcome],pr))

	0	1
0	29	1
1	5	26

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.902	0.798	0.963
3	se	0.839	0.663	0.945
4	sp	0.967	0.828	0.999
6	diag.or	150.800	16.521	1376.474

par(op)
par(xpd = TRUE)
PCAdataframe[,outcome] <- factor(PCAdataframe[,outcome])
PCAmodel <- rpart(paste(outcome,"~."),PCAdataframe,control=rpart.control(maxdepth=3))
pr <- predict(PCAmodel,PCAdataframe,type = "class")
ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
if (length(unique(pr))>1)
{
  plot(PCAmodel,main="PCA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
  text(PCAmodel, use.n = TRUE,cex=0.75)
  ptab <- epiR::epi.tests(table(pr==0,PCAdataframe[,outcome]==0))
}

pander::pander(table(PCAdataframe[,outcome],pr))

	0	1
0	23	7
1	3	28

pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.836	0.719	0.918
3	se	0.903	0.742	0.980
4	sp	0.767	0.577	0.901
6	diag.or	30.667	7.117	132.134

par(op)

1.11.1 EFA

  EFAdataframe[,outcome] <- factor(EFAdataframe[,outcome])
  EFAmodel <- rpart(paste(outcome,"~."),EFAdataframe,control=rpart.control(maxdepth=3))
  pr <- predict(EFAmodel,EFAdataframe,type = "class")
  
  ptab <- list(er="Error",detail=matrix(nrow=6,ncol=1))
  if (length(unique(pr))>1)
  {
    plot(EFAmodel,main="EFA",branch=0.5,uniform = TRUE,compress = TRUE,margin=0.1)
    text(EFAmodel, use.n = TRUE,cex=0.75)
    ptab <- epiR::epi.tests(table(pr==0,EFAdataframe[,outcome]==0))
  }

  pander::pander(table(EFAdataframe[,outcome],pr))

	0	1
0	29	1
1	16	15

  pander::pander(ptab$detail[c(5,3,4,6),])

	statistic	est	lower	upper
5	diag.ac	0.721	0.592	0.829
3	se	0.484	0.302	0.669
4	sp	0.967	0.828	0.999
6	diag.or	27.188	3.282	225.207

  par(op)